The first CP model, constructed by Krugman (1991a, 1991b), is based on migration linkages. In it, manufacturing workers decide where they want to live based on their real wage. From (2.7) and the fact that the price of agricultural goods is normalized at one, we find that
ω = w
qà (2.10)
for real wageω.
Agricultural workers are supposed to stay put. To see how this changes the model, remember the hypothetical shock in demand of the previous paragraph: it led to a (disproportionally large) change in the number of firms, but there the causality stopped. Now, the changing number of firms will also, because of the variety effect, alter the price index of industrial
goods. This in turn affects real wages and will lead to migration. And the channel may not end there: we will have to trace the effects of this migration, to find out where, or whether, the process ends.
Neary (2001, p. 542) finds that there are three effects of a change in the number of firms in a region. The first is the competition effect: when there are more firms, each gets a smaller piece of total revenue. This effect does not depend on labor mobility and was already present in the model above.
It is a stabilizing force, in the sense that it limits the number of firms that can profitably enter after a shock in demand.
The second and third effect work through the mobile labor force. As the number of firms in a region increases, the increased scarcity of labor will drive up real wages, inducing migration into the region. This has two effects. Firstly, the new workers will demand manufactures from local producers. Thisdemand linkageleads to an increase in profitability. Neary (2001) shows that, assuming wages return to their prior levels, the balance of the first and the second effect depends on the relative sizes of à, the share of manufactures in demand, andZ, the index of transport costs de- fined in appendix 2.B. If à is larger, the (destabilizing) demand linkage dominates, while a largerZimplies that the (stabilizing) competition effect is stronger.14
However, we must also take into account that the decline in price index qcaused by the increasing number of firms, leads to a lower cost of living in the region where the demand shock took place. Since real wageωmust be equal in both regions, the assumption that wages return to their previous level must be false. Nominal wages can fall, leading to a further increase in profitability. This is the third effect.
The balance of (stabilizing) effect 1 versus (destabilizing) effects 2 and 3 determines whether a symmetric equilibrium, in which both regions have the same number of firms, can be stable. If a small demand shock in one region leads to a cumulative process of migration and firm entrance, the equilibrium is unstable; if instead it fails to lead to a cumulative process the equilibrium is stable. Using the properties of the model, we can derive a condition on the parameters that tells us whether the symmetric equilib- rium is stable or not. The level of transport costs at which stability changes is called thebreak pointτB.
Similarly, we can ask whether complete agglomeration is stable. That is, when all manufacturing is concentrated in one region, and there is a de- mand shock in the ‘empty’ region, does a cumulative process ensue which leads to a symmetric equilibrium? If not, the agglomeration is stable and
14This result is appealing: a largeZ corresponds to low costs of trade and diminishes the market power that producers exercise over local demand. With low costs of transport these consumers can easily substitute imported goods. A large value ofàindicates that consumers spend a big share of their income on manufactured goods, making their arrival more interesting to producers, but only to the extent that buying local goods is attractive.
the model returns to its previous state after the shock. There exist values of τ for which this is indeed the case, so that the model can explain endoge- nous agglomeration, as promised. However, for transport costs that are too high the equilibrium is not stable. Hence, a level of transport costs may be derived at which the stability of the concentrated equilibrium changes.
This level is called thesustain pointτS.
Both points are derived in appendix 2.C. It turns out that the sustain point and the break point are generally not the same, and thatτB > τS. This means that there exist transport costsτ+, withτB > τ+ > τS, where both the agglomerated and the symmetric equilibrium are stable. Which equilibrium actually occurs depends on the initial conditions: if the model starts off close to symmetric, the symmetric equilibrium will be attained. If the model starts out with all industry concentrated in one region, it stays that way. The CP model with transport costs τ+ has a path-dependent solution.
The intermediate goods-based CP model
Venables (1996a), in a model where labor is not mobile, shows that it is possible that input-output linkages between firms fulfill the same role as a mobile workforce. Using a monopolistic competition setup for both an upstream and a downstream sector, Venables shows that it is possible that an increase in the size of one industry brings the other industry to a higher level of efficiency. The model’s conclusions remain the same in Krugman and Venables (1995), who extend the framework by collapsing the upstream and downstream industries into one layer. The monopolistic competitive market structure is preserved by a specific form of the final demand func- tion. Amiti (1997) shows that a similar outcome may be obtained without the use of an MC framework. In her model, a scale effect arises because of a pricing game that is played between firms in a sector. An increase in the number of firms has a negative effect on collusion and ups the sector’s efficiency.
Later in this book, we will make good use of the model where inter- mediate goods transmit the complementarity between firms. A detailed introduction to this model can be found in chapters 3 and 4.
Intertemporal linkages and the CP model
Aspects of factor accumulation can also serve as a medium for agglom- erative tendencies. Baldwin and Martin (2003) survey the interdependen- cies between agglomeration and growth; they divide the subject into two classes: in the first class, growth influences agglomeration but there is no causality going the other way. We will discuss this class in the current para- graph, as it illustrates how the accumulation of capital can lead to agglom-
eration. The other class, in which technological spillovers are only local, will be discussed after our introduction to growth theory below. In models of the second class, agglomeration can affect the rate of growth, and vice versa. They are the subject of section 2.5 on dynamic economic geography.
Assume that there exist knowledge spillovers, and that they are global.
That is, the cost of capital investment declines as a function of the world stock of capital. In that case,
K˙i =γãLIi ãKworld (2.11)
where the growth of the capital (or ‘knowledge’) stock of regionidepends on the number of people working in the innovation sector,LIand the world stock of capitalKworld.
Whether capital accumulation of this kind can lead to full agglomera- tion depends on the mobility of capital. If we assume that inhabitants of one region can own and operate capital in another region, while spending the proceeds at home, capital is mobile. If instead we assume that most cap- ital takes the form of human knowledge, which cannot be separated from its owner, capital is immobile.
Baldwin and Martin (2003) show that with perfect mobility, the initial distribution of firms and capital between regions is stable. Both regions save and accumulate capital, deploying it where it is most productive. With zero capital mobility, however, agglomeration in one region can occur. This happens when trade costs are sufficiently low.
The reasoning behind agglomeration is the following: agents can only invest in capital that is used in their own region. The incentive to invest depends on the profitability of operating a firm; the firm’s profitability in turn depends on the demand for its products. Now if trade costs are high, local demand can be enough to sustain firms in either region. But with low trade costs, it is possible that one region enters into a downward spiral: if the number of firms declines, the income from capital declines (all capital is owned locally due to the immobility) which drives down local demand.
Meanwhile, imports from the other region substitute for products that are no longer available locally. This further decreases the incentive to invest in local capital. Ultimately then, all investments are made in the other region.